The following identity holds [1]},[2]},[3]},
\(&&\int _0^\nu d\xi _1\dots \int _0^\nu d\xi _n \sum _{r=1}^n \vec{k}_r^2 (\nu -\xi _r)\exp \left[\sum _{s=1}^n 2i\vec{p^{\prime }}\cdot \vec{k}_s(\nu -\xi _s)\right]=\nonumber \\&&\sum _{r=1}^n \vec{k}_r^2 \frac{\partial }{\partial (2i\vec{p^{\prime }}\cdot \vec{k}_r)}\prod _{s=1}^n \frac{-1}{2i\vec{p^{\prime }}\cdot \vec{k}_s}[1-e^{2i\nu \vec{p^\prime }\cdot \vec{k}_s}].\) 
